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Indefinite-Quadratic Estimation and Control

Indefinite-Quadratic Estimation and Control
A Unified Approach to H2 and H-infinity Theories

Part of Studies in Applied and Numerical Mathematics

  • Date Published: November 1998
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898714111


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About the Authors
  • This monograph presents a unified mathematical framework for a wide range of problems in estimation and control. The authors discuss the two most commonly used methodologies: the stochastic H2 approach and the deterministic (worst-case) H8 approach. Despite the fundamental differences in the philosophies of these two approaches, the authors have discovered that, if indefinite metric spaces are considered, they can be treated in the same way and are essentially the same. The benefits and consequences of this unification are pursued in detail, with discussions of how to generalize well-known results from H$^2$ theory to H$^\infty$ setting, as well as new results and insight, the development of new algorithms, and applications to adaptive signal processing. The authors deliberately have placed primary emphasis on estimation problems which enable one to solve all the relevant control problems in detail.

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    Product details

    • Date Published: November 1998
    • format: Hardback
    • isbn: 9780898714111
    • length: 572 pages
    • dimensions: 260 x 185 x 35 mm
    • weight: 1.237kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    1. Introduction and motivation
    2. Linear estimation in Krein spaces
    3. State-space models in Krein space
    4. Finite-horizon H8 filtering
    5. Array algorithms
    6. Several related problems
    7. H8 Optimality of the LMS algorithm
    8. Duality
    9. Finite-horizon control problems
    10. Input-output approach to H2 and H8 estimation
    11. Input-output approach to H2 and H8 control
    12. The discrete-time algebraic Riccati equation
    13. Infinite-Horizon results for state-space Models
    14. Asymptotic behavior
    15. Optimal H8 solutions
    16. Continuous-time results and final remarks

  • Authors

    Babak Hassibi

    Ali H. Sayed

    Thomas Kailath

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